Chosen Solution
PSP will not work without it charging and even then will randomly shut down and factory reset. Ive changed the battery numerous times and checked the charging output which at first, the charger that came with it was not supplying enough power to charge properly. I got a stronger cable (one that is recommended for the PSP through Sony) still have same issue
It can be an issue with the battery connector. The cable that connects the battery to the main board might by dirty and have corrosion which is causing the battery not to work. Get some isopropyl alcohol and clean the battery connector’s contacts and also the socket where the cable connectors. As to why it randomly shuts down I am not sure